Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If one leg of a right triangle is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b²; 10² = 8² + b²; 100 = 64 + b²; b² = 36; b = 6.

Front

What is the relationship between the angles of a right triangle and the Pythagorean Theorem?

Back

The Pythagorean Theorem is only applicable to right triangles, which have one angle measuring 90 degrees.

Front

How can the Pythagorean Theorem be used in real-life situations?

Back

It can be used to determine distances, such as finding the shortest path between two points, or in construction to ensure structures are level.

Front

What is the converse of the Pythagorean Theorem?

Back

If a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625 = 25².